Domination Critical Knodel Graphs
D. A. Mojdeh, S. R. Musawi, E. Nazari

TL;DR
This paper investigates the domination criticality and stability of Kn"odel graphs, characterizing 3-regular and 4-regular cases in terms of their domination number properties.
Contribution
It provides a characterization of the domination criticality and stability of Kn"odel graphs, focusing on 3-regular and 4-regular cases, which was previously unexplored.
Findings
Characterized 3-regular Kn"odel graphs as $oldsymbol{eta}$-critical or $oldsymbol{eta}$-stable.
Characterized 4-regular Kn"odel graphs as $oldsymbol{eta}$-critical or $oldsymbol{eta}$-stable.
Established conditions for domination criticality and stability in these graphs.
Abstract
A set of vertices of a graph is a dominating set if each vertex of is adjacent to some vertex of . The domination number of , , is the minimum cardinality of a dominating set of . A graph is called domination vertex critical, or just -critical if removal of any vertex decreases the domination number. A graph is called domination vertex stable, or just -stable, if removal of any vertex does not decrease the domination number. For an even integer and , a Kn\"odel graph is a -regular bipartite graph of even order , with vertices , for and , where for every , , there is an edge between vertex and every vertex (mod (n/2)), for . in this paper, we study…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
